None of the offered choices is correct.
The radical cannot be simplified. If rewritten, it must be written as something like
![x \sqrt[3]{ \frac{6}{x}}](https://tex.z-dn.net/?f=%20x%20%5Csqrt%5B3%5D%7B%20%5Cfrac%7B6%7D%7Bx%7D%7D%20)
or
![\frac{6x}{ \sqrt[3]{36x}}](https://tex.z-dn.net/?f=%20%5Cfrac%7B6x%7D%7B%20%5Csqrt%5B3%5D%7B36x%7D%7D%20)
The radical cannot be simplified. If rewritten, it must be written as something like
or
Find the area of the triangle
1 answer:
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Make a change of coordinates:
The Jacobian for this transformation is
and has a determinant of
Note that we need to use the Jacobian in the other direction; that is, we've computed
but we need the Jacobian determinant for the reverse transformation (from
to 
. To do this, notice that
we need to take the reciprocal of the Jacobian above.
The integral then changes to
The Jacobian for this transformation is
and has a determinant of
Note that we need to use the Jacobian in the other direction; that is, we've computed
but we need the Jacobian determinant for the reverse transformation (from
we need to take the reciprocal of the Jacobian above.
The integral then changes to